element distortion in finite element analysis相關(guān)參考內(nèi)容

elementdistortioninfiniteelementanalysis

Finiteelementanalysisisapowerfulnumericalmethodthatiscommonlyusedinengineeringtosolvecomplexproblemsrelatedtostructuraldesign.Inordertoobtainaccurateresultsfromfiniteelementanalysis,itisimportanttoensurethattheelementsusedintheanalysisarenotdistorted.Elementdistortionoccurswhenthegeometricshapeofanelementdeviatessignificantlyfromitsidealshape,whichcanleadtoerroneousresults.Inthisarticle,wewillexploretheconceptofelementdistortioninfiniteelementanalysisanditsimpactontheaccuracyofresults.

DefinitionofElementDistortion

Elementdistortionisameasureofhowdistortedanelementisfromitsidealshape.Infiniteelementanalysis,idealelementsareconstructedbyassumingthattheshapeoftheelementisthesameastheshapedescribedbythemathematicalfunctionsusedtomodeltheproblem.Inreality,duetogeometricandotherconstraints,itisimpossibletocreateidealelements.Elementdistortionoccurswhentheshapeofanelementdeviatesfromitsidealshapebyasignificantamount.

TypesofElementDistortion

Thereareseveraltypesofelementdistortionthatcanoccurinfiniteelementanalysis.Themostcommontypesinclude:

1.Jacobiandistortion:ThisoccurswhenthetransformationofidealelementcoordinatestotheactualelementcoordinatesresultsinaninvertedornegativeJacobianmatrix.Thiscanleadtonumericalinstabilityanderrorsinresults.

2.Aspectratiodistortion:Thisoccurswhentheaspectratioofanelement(i.e.theratioofitslongestsidetoitsshortestside)istoolargeortoosmall.Thiscanleadtopooraccuracyinresults.

3.Warpingdistortion:Thisoccurswhentheidealelementshapeiswarpedduetothepresenceofstiffenersorotherstructuralelements.Thiscanleadtoinaccuraciesinresultsastheidealelementshapeisnolongerrepresentativeoftheactualshape.

4.Skewdistortion:Thisoccurswhentheanglebetweenthesidesofanelementissignificantlydifferentfrom90degrees.Thiscanleadtoinaccuraciesinresultsastheelementisnolongeralignedwiththeglobalcoordinatesystem.

ImpactofElementDistortiononResults

Elementdistortioncanhaveasignificantimpactontheaccuracyofresultsobtainedfromfiniteelementanalysis.Themagnitudeofthisimpactdependsontheseverityofthedistortionandthetypeofanalysisbeingperformed.Ingeneral,thefollowingeffectscanbeexpected:

1.Reducedaccuracy:Elementdistortioncanleadtoerrorsinresults,whichcanreducetheaccuracyoftheanalysis.Thiscanbeparticularlyproblematicincaseswherehighlevelsofaccuracyarerequired,suchasinthedesignofsafety-criticalstructures.

2.Reducedconvergence:Elementdistortioncanalsoleadtodecreasedconvergencerates,whichcanincreasethecomputationaltimerequiredtoobtainaccurateresults.

3.Inaccuratestressandstraindistributions:Elementdistortioncanleadtoinaccuratestressandstraindistributionswithinthestructure,whichcancompromisethesafetyandintegrityofthestructure.

4.Lossofelements:Inextremecasesofelementdistortion,someelementsmayneedtobedeletedfromtheanalysis,whichcanleadtoalossofaccuracyandanincreaseincomputationaltime.

StrategiestoMitigateElementDistortion

Thereareseveralstrategiesthatcanbeusedtomitigateelementdistortioninfiniteelementanalysis.Theseinclude:

1.Elementshapeoptimization:Elementscanbeoptimizedtoreducedistortionbyadjustingaspectratios,elementangles,andotherparameters.

2.Useofhigher-orderelements:Higher-orderelementscanbeusedtoreducetheimpactofelementdistortiononresults.

3.Meshrefinement:Meshrefinementcanbeusedtoreduceelementdistortionbyincreasingthenumberofelementsinareasofthestructurewheredistortionishighest.

4.Useofalternativeelementtypes:Alternativetypesofelements,suchastetrahedronsorhexahedrons,canbeusedtoreduceelementdistortion.

Conclusion

Elementdistortionisacommonissueinfiniteelementanalysisthatcanhaveasignificantimpactontheaccuracyofresults.Understandingthetypesandcausesofelementdistortionisimportantinordertoimplementeffectivest